Nonlinear Dynamics of Spherical Caps

Abstract

AbstractIn the present work, the nonlinear vibrations of shallow spherical caps, under the action of static and fluctuating pressure, are studied. A semi-analytical approach, based on the Novozhilov’s nonlinear thin shell theory, is developed; the approach is suitable for treating homogeneous isotropic shells. A meshless method is considered to reduce the partial differential equations (PDEs) to a set of ordinary differential equations (ODEs): the displacement fields are expanded through a mixed series of Legendre polynomials and harmonic functions in the meridional and circumferential directions respectively. The ODEs are obtained by taking advantage from the Lagrange equations and are numerically analyzed using continuation and direct integration techniques. The achievements of this study show that nonlinear modal interactions can lead to the activation of non-symmetric vibrational states.KeywordsSpherical capNonlinear vibrationsBifurcation analysis